Retrofocus type wide angle lens of low F-number

ABSTRACT

A wide angle lens of high performance comprising twelve lenses grouped in ten components which satisfies the following four conditions: 
     
         F/1.8 &lt;| F.sub. 1.2.3.4|&lt; F/1.1, F.sub.1.2.3.4. &lt; 0  (1) 
    
     
         F/0.6 &lt;| F.sub.1.2.3.4.5.6 |&lt; F/0.15, F.sub.1.2.3.4.5.6 &lt; 
    
      0                                                          (2i) 
     
         F/1.4 &lt;F.sub.1.2.3.4.5.6.7 &lt;  F/0.8                         (2ii) 
    
     
          0.1 &lt; n.sub.8 - n.sub.9 &lt;0.2                               (3) 
    
     
          0.3.sub.l &lt; (d.sub.1 +  d.sub.2 + d.sub.3 + d.sub.4 + d.sub.5) &lt;  0.5  (4)

SUMMARY OF THE INVENTION

In the development in the retrofocus type lens, a wide angle lens of small F-number has been developed. This invention relates to a lens of this type, and more specifically to a lens having the angle of field of about 95° and the F-number of about 2.8. This is accomplished by providing a wide angle lens of high performance comprising twelve lenses grouped in ten components which satisfies the following four conditions:

    F/1.8 <|F.sub.1.2.3.4 |<  F/1.1, F.sub.1.2.3.4 < 0 (1)

    f/0.6 <|f.sub. 1.2.3.4.5.6 |<  f/0.15, f.sub. 1.2.3.4.5.6 < 0                                                       (2i)

    F/1.4 <F.sub. 1.2.3.4.5.6.7 < F/0.8                        (2ii)

    0.1 <n.sub.8 -n.sub.9 < 0.2                                (3)

    0.3 l< (d.sub.1 + d.sub.2 + d.sub.3  + d.sub.4 + d.sub.5) <0.5 l (4)

BRIEF DESCRIPTION OF THE DRAWINGS

The specific nature of the invention, as well as other objects, aspects, uses and advantages thereof, will clearly appear from the following description and from the accompanying drawings, in which:

FIG. 1 is a view showing the lens system in accordance with the first embodiment of the invention including a filter,

FIGS. 2a to 2d show aberration curves obtained by the lens system in accordance with the first embodiment of the invention,

FIG. 3 is a view showing the lens system in accordance with the second embodiment of the invention including a filter, and

FIGS. 4a to 4d show aberration curves obtained by the lens system in accordance with the second embodiment of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Describing the construction of the lens first, the first lens is a negative lens, the second lens is a positive lens, the third and the fourth lenses are negative meniscus lenses concave to the image side, the fifth and the sixth lenses constitute a cemented lens, and a filter is located between the fourth lens and the fifth lens. The seventh lens is a positive lens, the eighth lens is a negative lens, and the nineth lens is a positive lens which is cemented with the eighth lens. The tenth lens is a positive lens, the eleventh lens is a negative meniscus lens, and the twelfth lens is a positive lens.

The features of the lens in accordance with the present invention are as follows:

    F/1.8 <|F.sub. 1.2.3.4 |< F/1.1, F.sub. 1.2.3.4 <0 (1)

    f/0.6 <|f.sub. 1.2.3.4.5.6 |< f/0.15, f.sub. 1.2.3.4.5.6 <0                                                        (2i)

    F/1.4 <F.sub. 1.2.3.4.5.6.7 < F/0.8                        (2ii)

    0.1 <n.sub.8 - n.sub.9 < 0.2                               (3)

    0.3l<(d.sub.1 + d.sub.2 + d.sub.3 + d.sub.4 + d.sub.5)<0.5l (4)

wherein the characters designate dimensions as follows:

F: composite focal length

F₁.2 . . . . . . _(i) : composite focal length of the lens system consisting of the first to the i-th lenses

d_(j) : the j-th spacing or lens thickness

r_(k) : radius of curvature of the k-th surface

n_(i) : refractive index for d-line of the i-th lens

ν_(i) : Abbe's number of the i-th lens

l: total length of the lens

f_(B) : back focal length.

Now the features of the lens of this invention as described above will be described in detail.

The first feature (1) defines a front negative lens system consisting of the front four lenses which refracts the light incident thereto at a wide angle to make it incident to the fifth lens at a comparatively small angle. This is to be defined with reference to the range of F-number of the lens. When the focal length |F₁ . 2 . 3 . 4 | is short over F/1.8, the load on the fifth lens and the lenses therebehind is reduced. However, when aperture efficiency is in the range of practically useful levels within the range of F-number not less than 2.8, the coma aberration is possibly deteriorated. When, to the contrary, the focal length of the lens system consisting of the four lenses is longer than that corresponding to F/1.1, the load on the fifth lens and the lenses therebehind become severe with respect to the long back focus and the wide angle of field, which is disadvantageous from the viewpoint of the whole system.

The second features (2)(i) and (ii) define the power of the seventh lens to compensate for a chromatic aberration of the lens system consisting of the first lens to the seventh lens which is determined with reference to the characteristic of the glass material of the fifth, sixth and seventh lenses. Further, these features are important for making a balance of aberration in the lens system consisting of the front seven lenses. When |F₁ . 2 . 3 . 4 . 5 . 6 | is shorter than the focal length corresponding to F/0.6, requirements for the seventh lens become severe when the focal length F₁ . 2 . 3 . 4 . 5 . 6 . 7 is shorter than the focal length corresponding to the F/1.4. The severe requirements make the manufacture of the lenses difficult. Further, owing to the extreme compensation, the aberration of unnatural form which is very difficult to be compensated for appears. When the focal length |F₁ . 2 . 3 . 4 . 5 . 6 | is shorter than that corresponding to F/0.6, a long back focus can be comparatively easily obtained, but the lenses behind the seventh lens are required to have higher positiveness. To the contrary, when the focal length is longer than that corresponding to F/0.15, a long back focal length cannot be obtained easily. In addition, in this case, the positiveness of the seventh lens is small and the compensation for the coma for the light of comparatively small incident angle becomes difficult in combination with the eighth and ninth lenses. When the focal length F₁ . 2 . 3 . 4 . 5 . 6 . 7 is shorter than that corresponding to F/1.4, the compensation by the eighth and ninth lenses become extremely large, which is undesirable from the viewpoint of compensation of aberration. When the focal length is longer than that corresponding to F/0.8, the compensation becomes insufficient, and Petzval sum increases.

The third feature (3) defines a difference in the refractive index for compensating the spherical aberration and properly compensating the coma aberration. This feature is important for properly compensating the coma of chromatic aberration and balance the chromatic aberration of the whole lens system in connection with the value ν and the radius of curvature.

The fourth feature (4) defines the relation between the aberrations and the length of the lens system. That is, when the length of the lens system is smaller than 0.3 l, the purpose for making the lens system short is satisfied with reference to the first feature and the second feature (2) i), but the aberration is deteriorated. When the length of the lens system is longer than 0.5 l, the aberration is improved but the overall length of the lens system becomes too long. If the rear lens component is made small to solve this problem, the balance in aberrations is deteriorated.

Two specific examples of the present invention will be described hereinbelow.

The first example is shown in FIG. 1 and consists of a negative meniscus lens L₁, a thick double convex lens L₂, a negative meniscus lens L₃, a negative meniscus lens L₄, a first cemented doublet consisting of a negative meniscus lens L₅ and a double convex lens L₆, a double convex lens L₇, a second cemented doublet consisting of a plano-concave lens L₈ and a positive meniscus lens L₉, a double convex lens L₁₀, a negative meniscus lens L₁₁, and a plano-convex lens L₁₂. A filter is inserted between lenses L₄ and L₅. The radii r₁ to r₂₂ and the thickness and separations d₁ to d₂₁, along with refractive indices n₁ to n₁₂ and Abbe numbers ν₁ to ν₁₂ for lenses L₁ to L₁₂ are given in Table I as follows:

                  TABLE 1                                                          ______________________________________                                         F = 100                                                                        F.sub.1.2.3.4 = -70.42                                                         F.sub.1.2.3.4.5.6 = -274.72                                                    F.sub.1.2.3.4.5.6.7 =  108.22                                                  f.sub.B = 178.14                                                                     Radius of  Lens Thickness                                                                             Refractive                                                                              Abbe                                     Lens  Curvature r                                                                               or Distance d                                                                              index n  No. ν                                 ______________________________________                                               r.sub.1 = 324.0                                                          L.sub.1 {        d.sub.1 = 5.82                                                                             n.sub.1 =1.6400                                                                         ν.sub.1 = 60.2                              r.sub.2 = 126.0                                                                           d.sub.2 = 54.94                                                     r.sub.3 = 3321.8                                                         L.sub.2          d.sub.3 = 139.21                                                                           n.sub.2 = 1.6204                                                                        ν.sub.2 = 60.3                              r.sub.4 = -350.9                                                                          d.sub.4 = 0.48                                                      r.sub.5 = 119.7                                                          L.sub.3          d.sub.5 = 10.19                                                                            n.sub.3 = 1.5119                                                                        ν.sub.3 = 58.1                              r.sub.6 = 58.5                                                                            d.sub.6 = 28.29                                                     r.sub.7 =  189.8                                                         L.sub.4          d.sub.7 = 14.56                                                                            n.sub.4 = 1.8160                                                                        ν.sub.4 = 46.8                              r.sub.8 = 86.5                                                                            d.sub.8.sub.-1 = 12.13                                              filter                                                                                    filter thick-                                                                  ness = 3.88                                                                    d.sub.8.sub.-2 = 4.85                                               r.sub.9 = 487.4                                                          L.sub.5          d.sub.9 = 11.26                                                                            n.sub.5 = 1.8074                                                                        ν.sub.5 = 35.4                              r.sub.10 = 216.3                                                         L.sub.6          d.sub.10 = 28.73                                                                           n.sub.6 = 1.7407                                                                        ν.sub.6 = 27.8                              r.sub.11 = -189.7                                                                         d.sub.11 = 7.76                                                     r.sub.12 = 159.7                                                         L.sub.7          d.sub.12 = 26.74                                                                           n.sub.7 = 1.5892                                                                        ν.sub.7 = 41.1                              r.sub.13 = -236.3                                                                         d.sub.13 = 5.67                                                     r.sub.14 = ∞                                                       L.sub.8          d.sub.14  = 11.40                                                                          n.sub.8 = 1.8051                                                                        ν.sub.8 = 25.4                              r.sub.15 = 95.5                                                          L.sub.9          d.sub.15 = 10.63                                                                           n.sub.9 = 1.6393                                                                        ν.sub.9 = 44.9                              r.sub.16 = 202.0                                                                          d.sub.16 = 7.18                                                     r.sub.17 = 4078.3                                                        L.sub.10         d.sub.17 = 15.48                                                                           n.sub.10 = 1.6170                                                                       ν.sub.10 = 62.8                             r.sub.18 = 110.2                                                                          d.sub.18 = 0.97                                                     r.sub.19 = 324.2                                                         L.sub.11         d.sub.19 = 7.28                                                                            n.sub.11 = 1.8051                                                                       ν.sub.11 = 25.4                             r.sub.20 = 108.8                                                                          d.sub.20 = 14.27                                                    r.sub.21 = ∞                                                       L.sub.12         d.sub.21 = 14.02                                                                           n.sub.12 = 1.7865                                                                       ν.sub.12 = 50.2                             r.sub.22 = -169.6                                                        ______________________________________                                    

FIG. 2a shows the spherical aberration; FIG. 2b shows the chromatic aberration; FIG. ac shows the distortion; and FIG. 2d shows the astigmatism of the lens system shown in FIG. 1 and defined in Table I.

The second example is shown in FIG. 3 and consists of a negative meniscus lens L₁, a double convex lens L₂, a negative meniscus lens L₃, a negative meniscus lens L₄, a first cemented doublet consisting of a negative meniscus lens L₅ and a double convex lens L₆, a double convex lens L₇, a second cemented doublet consisting of a negative meniscus lens L₈ and a positive meniscus lens L₉, a positive meniscus lens L₁₀, a negative meniscus lens L₁₁, and a double convex lens L₁₂. A filter is inserted between lenses L₄ and L₅. The radii r₁ to R.sub. 12 and Abbe numbers ν₁ to ν₁₂ for lenses L₁ to L₁₂ are given in Table II as follows:

                  TABLE II                                                         ______________________________________                                         F = 100                                                                        F.sub.1.2.3.4 = -62.89                                                         F.sub.1.2.3.4.5.6 = -239.80                                                    F.sub.1.2.3.4.5.6.7 = 90.74                                                    f.sub.B = 183.95                                                                     Radius of  Lens Thickness                                                                             Refractive                                                                              Abbe                                     Lens  Curvature r                                                                               or Distance d                                                                              Index n  No. ν                                 ______________________________________                                               r.sub.1 = 219.2                                                          L.sub.1          d.sub.1 = 5.84                                                                             n.sub.1 = 1.6968                                                                        ν.sub.1 = 55.7                              r.sub.2 = 110.9                                                                           d.sub.2 = 78.58                                                     r.sub.3 = 2434.5                                                         L.sub.2          d.sub.3 = 39.00                                                                            n.sub.2 = 1.5955                                                                        ν.sub.2 = 39.2                              r.sub.4 = -369.4                                                                          d.sub.4 = 0.53                                                      r.sub.5 = 132.9                                                          L.sub.3          d.sub.5 = 8.91                                                                             n.sub.3 = 1.6237                                                                        ν.sub.3 = 46.9                              r.sub.6 = 59.3                                                                            d.sub.6  = 37.58                                                    r.sub.7 = 185.1                                                          L.sub.4          d.sub.7 = 14.60                                                                            n.sub.4 = 1.8061                                                                        ν.sub.4 = 40.8                              r.sub.8 = 85.4                                                                            d.sub.8.sub.-1 = 12.17                                              filter     filter thick-                                                                  ness = 3.89                                                                    d.sub.8.sub.-2 = 4.86                                               r.sub.9 = 420.8                                                          L.sub.5          d.sub.9 = 11.44                                                                            n.sub.5 = 1.8340                                                                        ν.sub.5 = 37.2                              r.sub.10 = 92.6                                                          L.sub.6          d.sub.10 = 20.88                                                                           n.sub.6 = 1.7552                                                                        ν.sub.6 = 27.5                              r.sub.11 = -165.7                                                                         d.sub.11 = 7.30                                                     r.sub.12 = 134.7                                                         L.sub.7          d.sub.12 = 24.34                                                                           n.sub.7 = 1.5892                                                                        ν.sub.7 = 41.1                              r.sub.13 = -211.6                                                                         d.sub.13 = 1.85                                                     r.sub.14 =  35056.8                                                      L.sub.8          d.sub.14 = 8.42                                                                            n.sub.8 = 1.8051                                                                        ν.sub.8 = 25.4                              r.sub.15 = 77.4                                                          L.sub.9          d.sub.15 = 13.13                                                                           n.sub.9 = 1.6700                                                                        ν.sub.9 = 47.3                              r.sub.16 = 169.7                                                                          d.sub.16 = 9.73                                                     r.sub.17 = -3408.3                                                       L.sub.10         d.sub.17 = 17.72                                                                           n.sub.10 = 1.6134                                                                       ν.sub.10 = 57.4                             r.sub.18 = -105.6                                                                         d.sub.18 = 0.43                                                                            n.sub.11 = 1.8466                                                                       ν.sub.11 = 23.9                             r.sub.19 = 299.0                                                         L.sub.11         d.sub.19 = 5.89                                                     r.sub.20 = 106.5                                                                          d.sub.20 = 14.60                                                                           n.sub.12 = 1.5891                                                                       ν.sub.12 = 61.1                             r.sub.21 = 841.8                                                         L.sub.12         d.sub.21 =  18.45                                                   r.sub.22 = -147.5                                                        ______________________________________                                    

FIG. 4a shows the spherical aberration; FIG. 4b shows the chromatic aberration; FIG. 4c shows the distortion; and FIG. 4d shows the astigmatism of the lens system shown in FIG. 3 and defined in Table II.

It will be apparent that the embodiments shown are only exemplary and that various modifications can be made in construction and arrangement within the scope of the invention as defined in the appended claims. 

What is claimed is:
 1. A wide angle lens comprising twelve lenses grouped in ten components which satisfies the following conditions:

    F/1.8 < |F.sub.1 . 2 . 3 . 4 | < F/1.1, F.sub.1 . 2 . 3 . 4 <  0                                                    (1)

    f/0.6 < |f.sub.1 . 2 . 3 . 4 . 5 . 6 | < f/0.15, f.sub.1 . 2 . 3 . 4 . 5 . 6 <  0                                  ( 2i)

    F/1.4 < F.sub.1 . 2 . 3 . 4 . 5 . 6 . 7 < F/0.8            (2ii)

    0.1 < n.sub.8 - n.sub.9 <  0.2                             (3)

    0.3 l < (d.sub.1 + d.sub.2 + d.sub.3 + d.sub.4 + d.sub.5) < 0.5 l (4)

wherein the characters designate dimensions as follows: F: composite focal length F₁ . 2 ....... i : composite focal length of the lens system: consisting of the first to the i-th lenses d_(j) : the j-th spacing or lens thickness n_(i) : refractive index for d-line of the i-th lens l: total length of the lensthe first lens is a negative meniscus lens, the second lens is a thick double convex lens, the third and fourth lenses are negative meniscus lenses concave to the image side, the fifth and sixth lenses constitute a cemented doublet with the fifth lens being a negative meniscus lens and the sixth lens being a double convex lens, the seventh lens is a double convex lens, the eighth lens is a plano-concave lens, the ninth lens is a positive meniscus lens cemented with said eighth lens, the tenth lens is a double convex lens, the eleventh lens is a negative meniscus lens, and the twelfth lens is a plano-convex lens, and further comprising a filter located between said fourth lens and said fifth lens wherein the radii r₁ to r₂₂, the thicknesses and separations d₁ to d₂₁, the refractive indices n₁ to n₁₂, and Abbe numbers ν₁ to ν₁₂ of said first to twelfth lenses L₁ to L₁₂, respectively, satisfy the following conditions:

    F = 100                                                                        F.sub.1.2.3.4 = -70.42                                                         F.sub.1.2.3.4.5.6 = -274.72                                                    F.sub.1.2.3.4.5.6.7 = 108.22                                                   (back focal length)                                                            f.sub.B = 178.14                                                                     Radius of  Lens Thickness                                                                             Refractive                                                                              Abbe                                     Lens  Curvature r                                                                               or Distance d                                                                              index n  No. ν                                 ______________________________________                                               r.sub.1 = 324.0                                                          L.sub.1          d.sub.1 = 5.82                                                                             n.sub.1 = 1.6400                                                                        ν.sub.1 = 60.2                              r.sub.2 = 126.0                                                                           d.sub.2 = 54.94                                                     r.sub.3 = 3321.8                                                         L.sub.2          d.sub.3 = 139.21                                                                           n.sub.2 = 161 1.6204                                                                    ν.sub.2 = 60.3                              r.sub.4 = -350.9                                                                          d.sub.4 = 0.48                                                      r.sub.5 = 119.7                                                          L.sub.3          d.sub.5 = 10.19                                                                            n.sub.3 = 1.5119                                                                        ν.sub.3 = 58.1                              r.sub.6 = 58.5                                                                            d.sub.6 = 28.29                                                     r.sub.7 =  189.8                                                         L.sub.4          d.sub.7 = 14.56                                                                            n.sub.4 = 1.8160                                                                        ν.sub.4 = 46.8                              r.sub.8 = 86.5                                                                            d.sub.8.sub.-1 = 12.13                                              filter                                                                                    filter thick-                                                                  ness = 3.88                                                                    d.sub.8.sub.-2 = 4.85                                               r.sub.9 = 487.4                                                          L.sub.5          d.sub.9 = 11.26                                                                            n.sub.5 = 1.8074                                                                        ν.sub.5 = 35.4                              r.sub.10 = 216.3                                                         L.sub.6          d.sub.10 = 28.73                                                                           n.sub.6 = 1.7407                                                                        ν.sub.6 = 27.8                              r.sub.11 = -189.7                                                                         d.sub.11 = 7.76                                                     r.sub.12 = 159.7                                                         L.sub.7          d.sub.12 = 26.74                                                                           n.sub.7 = 1.5892                                                                        ν.sub.7 = 41.1                              r.sub.13 = -236.3                                                                         d.sub.13 = 5.67                                                     r.sub.14 = ∞                                                       L.sub.8          d.sub.14 = 11.40                                                                           n.sub.8 =  1.8051                                                                       ν.sub.8 = 25.4                              r.sub.15 = 95.5                                                          L.sub.9          d.sub.15 = 10.63                                                                           n.sub.9 = 1.6393                                                                        ν.sub.9 = 44.9                              r.sub.16 = 202.0                                                                          d.sub.16 = 7.18                                                     r.sub.17 = 4078.3                                                        L.sub.10         d.sub.17 = 15.48                                                                           n.sub.10 = 1.6170                                                                       ν.sub.10 = 62.8                             r.sub.18 = 110.2                                                                          d.sub.18 = 0.97                                                     r.sub.19 = 324.2                                                         L.sub.11         d.sub.19 = 7.28                                                                            n.sub.11 = 1.8051                                                                       ν.sub.11 = 25.4                             r.sub.20 = 108.8                                                                          d.sub.20 = 14.27                                                    r.sub.21 = ∞                                                       L.sub.12         d.sub.21 = 14.02                                                                           n.sub.12 = 1.7865                                                                       ν.sub.12 = 50.2                             r.sub.22 = -169.6                                                        ______________________________________                                    


2. A wide angle lens comprising twelve lenses grouped in ten components which satisfies the following conditions:

    F/1.8 < |F.sub.1 . 2 . 3 . 4 | < F/1.1, F.sub.1 . 2 . 3 . 4 <  0                                                    (1)

    f/0.6 < |f.sub.1 . 2 . 3 . 4 . 5 . 6 | < f/0.15, f.sub.1 . 2 . 3 . 4 . 5 . 6 <  0                                  (2i)

    F/1.4 < F.sub.1 . 2 . 3 . 4 . 5 . 6 . 7 < F/0.8            (2ii)

    0.1 < n.sub.8 -  n.sub.9 <  0.2                            (3)

    0.3 l < (d.sub.1 + d.sub.2 + d.sub.3 + d.sub.4 + d.sub.5) < 0.5 l (4)

wherein the characters designate dimensions as follows: F: composite focal length F₁ . 2 .......i : composite focal length of the lens system: consisting of the first to the i-th lenses d_(j) : the j-th spacing or lens thickness n_(i) : refractive index for d-line of the i-th lensl: total length of the lensthe first lens is a negative meniscus lens, the second lens is a double convex lens, the third and fourth lenses are negative meniscus lenses concave to the image side, the fifth and sixth lenses constitute a cemented doublet with the fifth lens being a negative meniscus lens and the sixth lens being a double convex lens, the seventh lens is a double convex lens, the eighth lens is a negative meniscus lens, the ninth lens is a positive meniscus lens cemented with said eighth lens, the tenth lens is a positive meniscus a lens, the eleventh lens is a negative meniscus lens, and the twelfth lens is a double convex lens, and further comprising a filter located between said fourth lens and said fifth lens wherein the radii r₁ to r₂₂, the thicknesses and separations d₁ to d₂₁, the refractive indices n₁ to n₁₂, and Abbe numbers ν₁ to ν₁₂ of said first to twelfth lenses L₁ to L₁₂, respectively, satisfy the following conditions:F = 100F₁.2.3.4 = -62.89F₁.2.3.4.5.6 = -239.80F₁.2.3.4.5.6.7 = 90.74(back focal length)f_(B) = 183.95 Radius of Lens Thickness Refractive AbbeLens Curvature r or Distance d Index n No. ν______________________________________ r₁ = 219.2L₁ d₁ = 5.84 n₁ = 1.698 ν₁ = 55.7 r₂ = 110.9 d₂ = 78.58 r₃ = 2434.5L₂ d₃ = 39.00 n₂ = 5955 ν₂ = 39.2 r₄ = -369.4 d₄ = 0.53 r₅ = 132.9L₃ d₅ = 8.91 n₃ = 1.6237 ν₃ = 46.9 r₆ = 59.3 d₆ = 37.58 r₇ = 185.1L₄ d₇ = 14.60 n₄ = 1.8061 ν₄ = 40.8 r₈ = 85.4 d₈ ₋₁ = 12.17 filter filter thick- ness = 3.89 d₈ ₋₂ = 4.86 r₉ = 420.8L₅ d₉ = 11.44 n₅ = 1.8340 ν₅ = 37.2 r₁₀ = 92.6L₆ d₁₀ = 20.88 n₆ = 1.7552 ν₆ = 27.5 r₁₁ = -165.7 d₁₁ = 7.30 r₁₂ = 134.7L₇ d₁₂ = 24.34 n₇ = 1.5892 ν₇ = 41.1 r₁₃ = -211.6 d₁₃ = 1.85 r₁₄ = 35056.8L₈ d₁₄ = 8.42 n₈ = 1.8051 ν₈ = 25.4 r₁₅ = 77.4L₉ d₁₅ = 13.13 n₉ = 1.6700 ν₉ = 47.3 r₁₆ = 169.7 d₁₆ = 9.73 r₁₇ = -3408.3L₁₀ d₁₇ = 17.72 n₁₀ = 1.6134 ν₁₀ = 57.4 r₁₈ = -105.6 d₁₈ = 0.43 n₁₁ = 1.8466 ν₁₁ = 23.9 r₁₉ = 299.0L₁₁ d₁₉ = 5.89 r₂₀ = 106.5 d₂₀ = 14.60 n₁₂ = 1.5891 ν₁₂ = 61.1 r₂₁ = 841.8L₁₂ d₂₁ = 18.45 r.sub. 22 = -147.5______________________________________ 